A bird flies according to mathematical principles, wrote Leonardo da Vinci in 1505. An assistant professor of aerospace engineering and a flight pilot, Henk Tennekes from the Free University at Amsterdam has written a book extending da Vinci's words. "After one has computed how large a swallow's wings should be," he writes, "one's respect for the magnitude of the mystery that keeps the bird in the air can only be greater."
Primarily aimed at students and fellow enthusiasts, Tennekes's book is a combination of raw enthusiasm, new research, fascinating anecdotes and a plethora of equations. Anything that flies is fair game when it comes to illustrating aircraft flight - from stag beetles to starlings, gulls to gliders, butterflies to Boeings, his favourite planes. His real aim is to inspire others to perform the calculations for themselves, following his careful and clear guidelines. As he says, "When I read a newspaper story about trains that require 1 megajoule of energy per passenger-kilometre, and then notice at the breakfast table that 100 grams of peanut butter supply 00 kilojoules, I cannot help calculating how much my train ticket would cost if the train ran on peanut butter rather than diesel oil or electricity."
Tennekes has created the "Great Flight Diagram" based on an idea first formulated by Galileo. The diagram covers anything with wings from the fruit fly, Drosophila melanogastor, which has a wingspan of 2 millimetres and weighs less than a milligram, to the Boeing 747. The 747 weighs 500 billion times as much as the fruit fly, yet flies only 100 times as fast - speed, as Tennekes shows, increases quite slowly with weight.
In the Great Flight Diagram, some birds and planes follow the Galileo-Tennekes specifications to a tee. These are the middle-of-the-road designs that avoid fancy engineering tricks. The starling, smack in the middle of the diagram, is an example of classic engineering - as is the Boeing, which has the exact wings to suit its size and weight. "The only thing that's special about the 747 is its weight," says Tennekes. "Not many birds weigh 350 tons."
Other birds and planes deviate from standard engineering practice - butterflies, owls and hang-gliders have oversize wings, making it easy for them to fly slowly. Yet others, like the smaller Boeing 737, and all jet fighters, have undersize wings, allowing them to keep up with bigger planes.
Tennekes likes these all-encompassing graphs. Specific energy consumption plotted against speed manages to include a budgie, a Ferrari, a Porsche, as well as other vehicles, and, of course, the ubiquitous 747. The diagram shows that when it comes to energy efficiency, budgies are bad flyers, gulls are as good as cars and flying becomes less expensive the faster you go. At high speeds, planes are fuel efficient. The reason is that planes, like trains and automobiles, suffer from aerodynamic resistance - drag from air as they move forwards. By being streamlined, some of this drag is reduced. But air resistance works on planes another way. As the plane flies, air is pushed down, which serves to give the plane added lift. At high speeds, this drag decreases and it is this that makes the Boeing economical. By flying fast, the Boeing has the same amount of drag as the slender-winged bird, the swift. The plane is so fuel efficient that over its working life a passenger mile costs just over a penny - which is a fifth as expensive as travelling by car. But then Tennekes may be a little biased: "The Boeing 747 is one of the engineering wonders of the world," he says, brimming with enthusiasm, "like the pyramids of Egypt, the Eiffel Tower or the Panama Canal." However, his enthusiasm does not cloud the clarity of his explanations, which cover the main topics on flight in a book for the mathematically inclined.
Sanjida O'Connell is a science writer, whose first novel, Theory of Mind, is published this month.
The Simple Science of Flight: From Insects to Jumbo Jets
Author - Henk Tennekes
ISBN - 0 262 20105 4
Publisher - MIT Press
Price - £13.95
Pages - 137